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Theoretical comparison of three X-ray phase-contrast imaging techniques: propagation-based imaging, analyzer-based imaging and grating interferometryP. C. Diemoz, A. Bravin, and P. Coan »View Author Affiliations
P. C. Diemoz,1,2,*
A. Bravin,2
and P. Coan1,3
1Faculty of Physics, Ludwig-Maximilians-University München, 85748 Garching, Germany 2European Synchrotron Radiation Facility, 38043 Grenoble, France 3Faculty of Medicine, Ludwig-Maximilians-University München, 81377 Munich, Germany *Corresponding author: p.diemoz@ucl.ac.uk |
Optics Express, Vol. 20, Issue 3, pp. 2789-2805 (2012)
http://dx.doi.org/10.1364/OE.20.002789
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Abstract
Various X-ray phase-contrast imaging techniques have been developed and applied over the last twenty years in different domains, such as material sciences, biology and medicine. However, no comprehensive inter-comparison exists in the literature. We present here a theoretical study that compares three among the most used techniques: propagation-based imaging (PBI), analyzer-based imaging (ABI) and grating interferometry (GI). These techniques are evaluated in terms of signal-to-noise ratio, figure of merit and spatial resolution. Both area and edge signals are considered. Dependences upon the object properties (absorption, phase shift) and the experimental acquisition parameters (energy, system point-spread function etc.) are derived and discussed. The results obtained from this analysis can be used as the reference for determining the most suitable technique for a given application.
© 2012 OSA
OCIS Codes
(100.2960) Image processing : Image analysis
(110.2990) Imaging systems : Image formation theory
(110.4980) Imaging systems : Partial coherence in imaging
(110.7440) Imaging systems : X-ray imaging
ToC Category:
Imaging Systems
History
Original Manuscript: October 17, 2011
Manuscript Accepted: November 30, 2011
Published: January 23, 2012
Virtual Issues
Vol. 7, Iss. 3 Virtual Journal for Biomedical Optics
Citation
P. C. Diemoz, A. Bravin, and P. Coan, "Theoretical comparison of three X-ray phase-contrast imaging techniques: propagation-based imaging, analyzer-based imaging and grating interferometry," Opt. Express 20, 2789-2805 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-3-2789
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- E. Castelli, M. Tonutti, F. Arfelli, R. Longo, E. Quaia, L. Rigon, D. Sanabor, F. Zanconati, D. Dreossi, A. Abrami, E. Quai, P. Bregant, K. Casarin, V. Chenda, R. H. Menk, T. Rokvic, A. Vascotto, G. Tromba, and M. A. Cova, “Mammography with synchrotron radiation: first clinical experience with phase-detection technique,” Radiology259(3), 684–694 (2011). [CrossRef] [PubMed]
- F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, and A. Vacchi, “Mammography of a phantom and breast tissue with synchrotron radiation and a linear-array silicon detector,” Radiology208(3), 709–715 (1998). [PubMed]
- G. Schulz, T. Weitkamp, I. Zanette, F. Pfeiffer, F. Beckmann, C. David, S. Rutishauser, E. Reznikova, and B. Mueller, “High-resolution tomographic imaging of a human cerebellum: comparison of absorption and grating-based phase contrast,” J. R. Soc. Interface7(53), 1665–1676 (2010). [CrossRef] [PubMed]
- F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys.2(4), 258–261 (2006). [CrossRef]
- T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13(16), 6296–6304 (2005). [CrossRef] [PubMed]
- C. David, B. Nöhammer, H. Solak, and E. Ziegler, “Differential X-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett.81(17), 3287–3289 (2002). [CrossRef]
- F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, and A. Vacchi, “Mammography of a phantom and breast tissue with synchrotron radiation and a linear-array silicon detector,” Radiology208(3), 709–715 (1998). [PubMed]
- P. C. Diemoz, P. Coan, I. Zanette, A. Bravin, S. Lang, C. Glaser, and T. Weitkamp, “A simplified approach for computed tomography with an X-ray grating interferometer,” Opt. Express19(3), 1691–1698 (2011). [CrossRef] [PubMed]
- P. Coan, F. Bamberg, P. C. Diemoz, A. Bravin, K. Timpert, E. Mützel, J. G. Raya, S. Adam-Neumair, M. F. Reiser, and C. Glaser, “Characterization of osteoarthritic and normal human patella cartilage by computed tomography X-ray phase-contrast imaging: a feasibility study,” Invest. Radiol.45(7), 437–444 (2010). [PubMed]
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- E. Castelli, M. Tonutti, F. Arfelli, R. Longo, E. Quaia, L. Rigon, D. Sanabor, F. Zanconati, D. Dreossi, A. Abrami, E. Quai, P. Bregant, K. Casarin, V. Chenda, R. H. Menk, T. Rokvic, A. Vascotto, G. Tromba, and M. A. Cova, “Mammography with synchrotron radiation: first clinical experience with phase-detection technique,” Radiology259(3), 684–694 (2011). [CrossRef] [PubMed]
- E. Castelli, M. Tonutti, F. Arfelli, R. Longo, E. Quaia, L. Rigon, D. Sanabor, F. Zanconati, D. Dreossi, A. Abrami, E. Quai, P. Bregant, K. Casarin, V. Chenda, R. H. Menk, T. Rokvic, A. Vascotto, G. Tromba, and M. A. Cova, “Mammography with synchrotron radiation: first clinical experience with phase-detection technique,” Radiology259(3), 684–694 (2011). [CrossRef] [PubMed]
- F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, and A. Vacchi, “Mammography of a phantom and breast tissue with synchrotron radiation and a linear-array silicon detector,” Radiology208(3), 709–715 (1998). [PubMed]
- F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, and A. Vacchi, “Mammography of a phantom and breast tissue with synchrotron radiation and a linear-array silicon detector,” Radiology208(3), 709–715 (1998). [PubMed]
- E. Castelli, M. Tonutti, F. Arfelli, R. Longo, E. Quaia, L. Rigon, D. Sanabor, F. Zanconati, D. Dreossi, A. Abrami, E. Quai, P. Bregant, K. Casarin, V. Chenda, R. H. Menk, T. Rokvic, A. Vascotto, G. Tromba, and M. A. Cova, “Mammography with synchrotron radiation: first clinical experience with phase-detection technique,” Radiology259(3), 684–694 (2011). [CrossRef] [PubMed]
- E. Pagot, S. Fiedler, P. Cloetens, A. Bravin, P. Coan, K. Fezzaa, J. Baruchel, J. Härtwig, K. von Smitten, M. Leidenius, M. L. Karjalainen-Lindsberg, and J. Keyriläinen, “Quantitative comparison between two phase contrast techniques: diffraction enhanced imaging and phase propagation imaging,” Phys. Med. Biol.50(4), 709–724 (2005). [CrossRef] [PubMed]
- D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol.42(11), 2015–2025 (1997). [CrossRef] [PubMed]
- P. C. Diemoz, P. Coan, I. Zanette, A. Bravin, S. Lang, C. Glaser, and T. Weitkamp, “A simplified approach for computed tomography with an X-ray grating interferometer,” Opt. Express19(3), 1691–1698 (2011). [CrossRef] [PubMed]
- G. Schulz, T. Weitkamp, I. Zanette, F. Pfeiffer, F. Beckmann, C. David, S. Rutishauser, E. Reznikova, and B. Mueller, “High-resolution tomographic imaging of a human cerebellum: comparison of absorption and grating-based phase contrast,” J. R. Soc. Interface7(53), 1665–1676 (2010). [CrossRef] [PubMed]
- F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys.2(4), 258–261 (2006). [CrossRef]
- T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13(16), 6296–6304 (2005). [CrossRef] [PubMed]
- T. E. Gureyev, Y. I. Nesterets, A. W. Stevenson, P. R. Miller, A. Pogany, and S. W. Wilkins, “Some simple rules for contrast, signal-to-noise and resolution in in-line x-ray phase-contrast imaging,” Opt. Express16(5), 3223–3241 (2008). [CrossRef] [PubMed]
- Y. I. Nesterets, P. Coan, T. E. Gureyev, A. Bravin, P. Cloetens, and S. W. Wilkins, “On qualitative and quantitative analysis in analyser-based imaging,” Acta Crystallogr. A62(4), 296–308 (2006). [CrossRef] [PubMed]
- T. E. Gureyev and S. W. Wilkins, “Regimes of X-ray phase-contrast imaging with perfect crystals,” Nuovo Cimento D19(2-4), 545–552 (1997). [CrossRef]
- S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature384(6607), 335–338 (1996). [CrossRef]
- E. Castelli, M. Tonutti, F. Arfelli, R. Longo, E. Quaia, L. Rigon, D. Sanabor, F. Zanconati, D. Dreossi, A. Abrami, E. Quai, P. Bregant, K. Casarin, V. Chenda, R. H. Menk, T. Rokvic, A. Vascotto, G. Tromba, and M. A. Cova, “Mammography with synchrotron radiation: first clinical experience with phase-detection technique,” Radiology259(3), 684–694 (2011). [CrossRef] [PubMed]
- P. C. Diemoz, P. Coan, I. Zanette, A. Bravin, S. Lang, C. Glaser, and T. Weitkamp, “A simplified approach for computed tomography with an X-ray grating interferometer,” Opt. Express19(3), 1691–1698 (2011). [CrossRef] [PubMed]
- G. Schulz, T. Weitkamp, I. Zanette, F. Pfeiffer, F. Beckmann, C. David, S. Rutishauser, E. Reznikova, and B. Mueller, “High-resolution tomographic imaging of a human cerebellum: comparison of absorption and grating-based phase contrast,” J. R. Soc. Interface7(53), 1665–1676 (2010). [CrossRef] [PubMed]
- E. Förster, K. Goetz, and P. Zaumseil, “Double crystal diffractometry for the characterization of targets for laser fusion experiments,” Krist. Tech.15(8), 937–945 (1980). [CrossRef]
- D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol.42(11), 2015–2025 (1997). [CrossRef] [PubMed]
- T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13(16), 6296–6304 (2005). [CrossRef] [PubMed]
- C. David, B. Nöhammer, H. Solak, and E. Ziegler, “Differential X-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett.81(17), 3287–3289 (2002). [CrossRef]
Acta Crystallogr. A
- Y. I. Nesterets, P. Coan, T. E. Gureyev, A. Bravin, P. Cloetens, and S. W. Wilkins, “On qualitative and quantitative analysis in analyser-based imaging,” Acta Crystallogr. A62(4), 296–308 (2006). [CrossRef] [PubMed]
Appl. Opt.
- A. Olivo, K. Ignatyev, P. R. T. Munro, and R. D. Speller, “Noninterferometric phase-contrast images obtained with incoherent x-ray sources,” Appl. Opt.50(12), 1765–1769 (2011). [CrossRef] [PubMed]
Appl. Phys. Lett.
- U. Bonse and M. Hart, “An X-ray interferometer,” Appl. Phys. Lett.6(8), 155–156 (1965). [CrossRef]
- C. David, B. Nöhammer, H. Solak, and E. Ziegler, “Differential X-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett.81(17), 3287–3289 (2002). [CrossRef]
Invest. Radiol.
- P. Coan, F. Bamberg, P. C. Diemoz, A. Bravin, K. Timpert, E. Mützel, J. G. Raya, S. Adam-Neumair, M. F. Reiser, and C. Glaser, “Characterization of osteoarthritic and normal human patella cartilage by computed tomography X-ray phase-contrast imaging: a feasibility study,” Invest. Radiol.45(7), 437–444 (2010). [PubMed]
J. Opt. Soc. Am.
- M. R. Teague, “Irradiance moments - their propagation and use for unique retrieval of phase,” J. Opt. Soc. Am.72(9), 1199–1209 (1982). [CrossRef]
J. Phys. D Appl. Phys.
- A. Bravin, “Exploiting the X-ray refraction contrast with an analyser: the state of the art,” J. Phys. D Appl. Phys.36(10A), A24–A29 (2003). [CrossRef]
- K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. I. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to x-ray phase-contrast imaging,” J. Phys. D Appl. Phys.37(19), 2746–2750 (2004). [CrossRef]
J. R. Soc. Interface
- G. Schulz, T. Weitkamp, I. Zanette, F. Pfeiffer, F. Beckmann, C. David, S. Rutishauser, E. Reznikova, and B. Mueller, “High-resolution tomographic imaging of a human cerebellum: comparison of absorption and grating-based phase contrast,” J. R. Soc. Interface7(53), 1665–1676 (2010). [CrossRef] [PubMed]
J. Synchrotron Radiat.
- P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, “Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction,” J. Synchrotron Radiat.12(2), 241–245 (2005). [CrossRef] [PubMed]
Krist. Tech.
- E. Förster, K. Goetz, and P. Zaumseil, “Double crystal diffractometry for the characterization of targets for laser fusion experiments,” Krist. Tech.15(8), 937–945 (1980). [CrossRef]
Med. Phys.
- J. M. Boone, K. K. Lindfors, V. N. Cooper, and J. A. Seibert, “Scatter/primary in mammography: comprehensive results,” Med. Phys.27(10), 2408–2416 (2000). [CrossRef] [PubMed]
Nat. Med.
- A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med.2(4), 473–475 (1996). [CrossRef] [PubMed]
Nat. Phys.
- F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys.2(4), 258–261 (2006). [CrossRef]
Nature
- S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature384(6607), 335–338 (1996). [CrossRef]
Nuovo Cimento D
- T. E. Gureyev and S. W. Wilkins, “Regimes of X-ray phase-contrast imaging with perfect crystals,” Nuovo Cimento D19(2-4), 545–552 (1997). [CrossRef]
Opt. Express
- P. C. Diemoz, P. Coan, I. Zanette, A. Bravin, S. Lang, C. Glaser, and T. Weitkamp, “A simplified approach for computed tomography with an X-ray grating interferometer,” Opt. Express19(3), 1691–1698 (2011). [CrossRef] [PubMed]
- T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13(16), 6296–6304 (2005). [CrossRef] [PubMed]
- T. E. Gureyev, Y. I. Nesterets, A. W. Stevenson, P. R. Miller, A. Pogany, and S. W. Wilkins, “Some simple rules for contrast, signal-to-noise and resolution in in-line x-ray phase-contrast imaging,” Opt. Express16(5), 3223–3241 (2008). [CrossRef] [PubMed]
Phys. Med. Biol.
- E. Pagot, S. Fiedler, P. Cloetens, A. Bravin, P. Coan, K. Fezzaa, J. Baruchel, J. Härtwig, K. von Smitten, M. Leidenius, M. L. Karjalainen-Lindsberg, and J. Keyriläinen, “Quantitative comparison between two phase contrast techniques: diffraction enhanced imaging and phase propagation imaging,” Phys. Med. Biol.50(4), 709–724 (2005). [CrossRef] [PubMed]
- D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol.42(11), 2015–2025 (1997). [CrossRef] [PubMed]
- J. Persliden and G. A. Carlsson, “Scatter rejection by air gaps in diagnostic radiology. Calculations using a Monte Carlo collision density method and consideration of molecular interference in coherent scattering,” Phys. Med. Biol.42(1), 155–175 (1997). [CrossRef] [PubMed]
Proc. SPIE
- M. Sanchez del Rio, C. Ferrero, and V. Mocella, “Computer simulations of bent perfect crystal diffraction profiles,” Proc. SPIE3152, 312–323 (1997), http://www.esrf.eu/UsersAndScience/Experiments/TBS/ SciSoft/xop2.3 . [CrossRef]
Radiology
- F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, and A. Vacchi, “Mammography of a phantom and breast tissue with synchrotron radiation and a linear-array silicon detector,” Radiology208(3), 709–715 (1998). [PubMed]
- E. Castelli, M. Tonutti, F. Arfelli, R. Longo, E. Quaia, L. Rigon, D. Sanabor, F. Zanconati, D. Dreossi, A. Abrami, E. Quai, P. Bregant, K. Casarin, V. Chenda, R. H. Menk, T. Rokvic, A. Vascotto, G. Tromba, and M. A. Cova, “Mammography with synchrotron radiation: first clinical experience with phase-detection technique,” Radiology259(3), 684–694 (2011). [CrossRef] [PubMed]
Rev. Sci. Instrum.
- A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibility of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum.66(12), 5486–5492 (1995). [CrossRef]
Spectrochim. Acta, Part B
- R. Tanuma and M. Ohsawa, “Submicron-resolved X-ray topography using asymmetric-reflection magnifiers,” Spectrochim. Acta, Part B59(10-11), 1549–1555 (2004). [CrossRef]
Other
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- M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, Cambridge, 1999).
2011, Olivo, Appl. Opt.
- E. Castelli, M. Tonutti, F. Arfelli, R. Longo, E. Quaia, L. Rigon, D. Sanabor, F. Zanconati, D. Dreossi, A. Abrami, E. Quai, P. Bregant, K. Casarin, V. Chenda, R. H. Menk, T. Rokvic, A. Vascotto, G. Tromba, and M. A. Cova, “Mammography with synchrotron radiation: first clinical experience with phase-detection technique,” Radiology259(3), 684–694 (2011). [CrossRef] [PubMed]
- P. Coan, F. Bamberg, P. C. Diemoz, A. Bravin, K. Timpert, E. Mützel, J. G. Raya, S. Adam-Neumair, M. F. Reiser, and C. Glaser, “Characterization of osteoarthritic and normal human patella cartilage by computed tomography X-ray phase-contrast imaging: a feasibility study,” Invest. Radiol.45(7), 437–444 (2010). [PubMed]
- G. Schulz, T. Weitkamp, I. Zanette, F. Pfeiffer, F. Beckmann, C. David, S. Rutishauser, E. Reznikova, and B. Mueller, “High-resolution tomographic imaging of a human cerebellum: comparison of absorption and grating-based phase contrast,” J. R. Soc. Interface7(53), 1665–1676 (2010). [CrossRef] [PubMed]
- F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys.2(4), 258–261 (2006). [CrossRef]
- Y. I. Nesterets, P. Coan, T. E. Gureyev, A. Bravin, P. Cloetens, and S. W. Wilkins, “On qualitative and quantitative analysis in analyser-based imaging,” Acta Crystallogr. A62(4), 296–308 (2006). [CrossRef] [PubMed]
- P. Coan, E. Pagot, S. Fiedler, P. Cloetens, J. Baruchel, and A. Bravin, “Phase-contrast X-ray imaging combining free space propagation and Bragg diffraction,” J. Synchrotron Radiat.12(2), 241–245 (2005). [CrossRef] [PubMed]
- E. Pagot, S. Fiedler, P. Cloetens, A. Bravin, P. Coan, K. Fezzaa, J. Baruchel, J. Härtwig, K. von Smitten, M. Leidenius, M. L. Karjalainen-Lindsberg, and J. Keyriläinen, “Quantitative comparison between two phase contrast techniques: diffraction enhanced imaging and phase propagation imaging,” Phys. Med. Biol.50(4), 709–724 (2005). [CrossRef] [PubMed]
- K. M. Pavlov, T. E. Gureyev, D. Paganin, Y. I. Nesterets, M. J. Morgan, and R. A. Lewis, “Linear systems with slowly varying transfer functions and their application to x-ray phase-contrast imaging,” J. Phys. D Appl. Phys.37(19), 2746–2750 (2004). [CrossRef]
- R. Tanuma and M. Ohsawa, “Submicron-resolved X-ray topography using asymmetric-reflection magnifiers,” Spectrochim. Acta, Part B59(10-11), 1549–1555 (2004). [CrossRef]
- A. Bravin, “Exploiting the X-ray refraction contrast with an analyser: the state of the art,” J. Phys. D Appl. Phys.36(10A), A24–A29 (2003). [CrossRef]
- C. David, B. Nöhammer, H. Solak, and E. Ziegler, “Differential X-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett.81(17), 3287–3289 (2002). [CrossRef]
- J. M. Boone, K. K. Lindfors, V. N. Cooper, and J. A. Seibert, “Scatter/primary in mammography: comprehensive results,” Med. Phys.27(10), 2408–2416 (2000). [CrossRef] [PubMed]
- F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, and A. Vacchi, “Mammography of a phantom and breast tissue with synchrotron radiation and a linear-array silicon detector,” Radiology208(3), 709–715 (1998). [PubMed]
- J. Persliden and G. A. Carlsson, “Scatter rejection by air gaps in diagnostic radiology. Calculations using a Monte Carlo collision density method and consideration of molecular interference in coherent scattering,” Phys. Med. Biol.42(1), 155–175 (1997). [CrossRef] [PubMed]
- M. Sanchez del Rio, C. Ferrero, and V. Mocella, “Computer simulations of bent perfect crystal diffraction profiles,” Proc. SPIE3152, 312–323 (1997), http://www.esrf.eu/UsersAndScience/Experiments/TBS/ SciSoft/xop2.3 . [CrossRef]
- T. E. Gureyev and S. W. Wilkins, “Regimes of X-ray phase-contrast imaging with perfect crystals,” Nuovo Cimento D19(2-4), 545–552 (1997). [CrossRef]
- D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol.42(11), 2015–2025 (1997). [CrossRef] [PubMed]
- A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nat. Med.2(4), 473–475 (1996). [CrossRef] [PubMed]
- S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature384(6607), 335–338 (1996). [CrossRef]
- A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibility of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum.66(12), 5486–5492 (1995). [CrossRef]
- E. Förster, K. Goetz, and P. Zaumseil, “Double crystal diffractometry for the characterization of targets for laser fusion experiments,” Krist. Tech.15(8), 937–945 (1980). [CrossRef]
- U. Bonse and M. Hart, “An X-ray interferometer,” Appl. Phys. Lett.6(8), 155–156 (1965). [CrossRef]
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